Jean-Yves Girard

Bio: Jean-Yves Girard is an academic researcher from Centre national de la recherche scientifique. The author has contributed to research in topics: Linear logic & Sequent calculus. The author has an hindex of 31, co-authored 59 publications receiving 10720 citations. Previous affiliations of Jean-Yves Girard include University of the Mediterranean & University of Paris.

Linear Logic: A Survey

Abstract: This introduction to linear logic is organised in four chapters: 1. Thesyntaxof linearlogic Here the formal system is introduced, with a special emphasis on the treatment of structural rules: weakening and contraction become logical rules for new connectives, 7 and !. Informal examples are introduced to illustrate this shift of viewpoint: linear logic is not about situations but about actions. 2. Thedenotational semantics of linear logic Coherent spaces (a drastic simplification of Scott domains) are introduced; semantically speaking, linear logic appears as a refinement of intuitionistic logic. 3. Proof-nets The specificities of linear logic (e.g., symmetries I/O) suggest a new kind of syntax for proofs, with intrinsic parallel features. Proof-nets are graphs (and not trees as usual) without explicit sequentialization; the difficult question is precisely that of the correcmess criterion, i.e., of the existence of implicit sequentialisations. 4. On the unity of logic This chapter is about logic (without adjective): from the experience gathered in linear logic, it seems possible to put all (decent) logical systems together. A sequent calculus LU is introduced: classical, intuitionistic and linear logics appear as fragments of this unified system. Many aspects of linear logic (especially applied ones) have been excluded from this approach; not because they are inessential, but because they do not fit with our pattern. We shall not try to make an enumeration (necessarily superficial) of these missing topics. Maybe the approach to linear logic though other authors (especially [Sv] and [T] which contain good bibliographies) is the best way to complete this initiation.

Linear logic and parallelism

Abstract: the paper discusses the relevance of a new logic called linear logic (Girard 1986) to computer science, and in particular to parallel computations. These general remarks will be detailed in a paper in preparation with Gianfranco Mascari.

Semantic parametricity in polymorphic lambda calculus

Abstract: A semantic condition necessary for the parametricity of polymorphic functions is considered One of its instances is the stability condition for elements of variable type in the coherent domains semantics A larger setting is presented that does not use retract pairs and keeps intact a basic feature of a certain function-type constructor Polymorphic lambda terms are semantically parametric because of normalization >

Normativity in Logic

Abstract: Incompleteness—the absence of alternative natural numbers—can be ascribed to a ready-made normativity, inducing a rigid departure syntax/semantics. Geometry of Interaction, set in the non-commutative universe of von Neumann algebras, makes normative assumptions explicit, thus rending possible their internalisation, a possible way out from the semantic aporia. As an illustration, we define an alternative “model”: logspace integers.

Editors' note: bibliometrics and the curators of orthodoxy

Abstract: Have you ever seen the Citation Indexes (CIs) for the year 1600? At that time, a very active community was working on the reconstruction of planetary movements by means of epicycles. In principle, any ellipse around the Sun may be approximated by sufficiently many epicycles around the Earth. This is a non-trivial geometrical task, especially given the lack of analytical tools (sums of series). And the books and papers of many talented geometers quoted one another. Scientific knowledge, however, was already taking other directions. Science has a certain ‘inertia’, it is prudent (at times, it has been exceedingly so, mostly for political or metaphysical reasons), but even under the best of conditions, we all know how difficult it is to accept new ideas, to let them blossom in time, away from short-term pressures.

Types and Programming Languages

Abstract: A type system is a syntactic method for automatically checking the absence of certain erroneous behaviors by classifying program phrases according to the kinds of values they compute. The study of type systems -- and of programming languages from a type-theoretic perspective -- has important applications in software engineering, language design, high-performance compilers, and security.This text provides a comprehensive introduction both to type systems in computer science and to the basic theory of programming languages. The approach is pragmatic and operational; each new concept is motivated by programming examples and the more theoretical sections are driven by the needs of implementations. Each chapter is accompanied by numerous exercises and solutions, as well as a running implementation, available via the Web. Dependencies between chapters are explicitly identified, allowing readers to choose a variety of paths through the material.The core topics include the untyped lambda-calculus, simple type systems, type reconstruction, universal and existential polymorphism, subtyping, bounded quantification, recursive types, kinds, and type operators. Extended case studies develop a variety of approaches to modeling the features of object-oriented languages.

Linear logic

Abstract: Linear logic was introduced by Girard in 1987 [11] . Since then many results have supported Girard' s statement, \"Linear logic is a resource conscious logic,\" and related slogans . Increasingly, computer scientists have come to recognize linear logic as an expressive and powerful logic with connection s to a variety of topics in computer science . This column presents a.n intuitive overview of linear logic, some recent theoretical results, an d summarizes several applications of linear logic to computer science . Other introductions to linear logic may be found in [12, 361 .

On understanding types, data abstraction, and polymorphism

Abstract: Our objective is to understand the notion of type in programming languages, present a model of typed, polymorphic programming languages that reflects recent research in type theory, and examine the relevance of recent research to the design of practical programming languages.Object-oriented languages provide both a framework and a motivation for exploring the interaction among the concepts of type, data abstraction, and polymorphism, since they extend the notion of type to data abstraction and since type inheritance is an important form of polymorphism. We develop a l-calculus-based model for type systems that allows us to explore these interactions in a simple setting, unencumbered by complexities of production programming languages.The evolution of languages from untyped universes to monomorphic and then polymorphic type systems is reviewed. Mechanisms for polymorphism such as overloading, coercion, subtyping, and parameterization are examined. A unifying framework for polymorphic type systems is developed in terms of the typed l-calculus augmented to include binding of types by quantification as well as binding of values by abstraction.The typed l-calculus is augmented by universal quantification to model generic functions with type parameters, existential quantification and packaging (information hiding) to model abstract data types, and bounded quantification to model subtypes and type inheritance. In this way we obtain a simple and precise characterization of a powerful type system that includes abstract data types, parametric polymorphism, and multiple inheritance in a single consistent framework. The mechanisms for type checking for the augmented l-calculus are discussed.The augmented typed l-calculus is used as a programming language for a variety of illustrative examples. We christen this language Fun because fun instead of l is the functional abstraction keyword and because it is pleasant to deal with.Fun is mathematically simple and can serve as a basis for the design and implementation of real programming languages with type facilities that are more powerful and expressive than those of existing programming languages. In particular, it provides a basis for the design of strongly typed object-oriented languages.

Proofs and types

Abstract: Sense, denotation and semantics natural deduction the Curry-Howard isomorphism the normalisation theorem Godel's system T coherence spaces denotational semantics of T sums in natural deduction system F coherence semantics of the sum cut elimination (Hauptsatz) strong normalisation for F representation theorem semantics of System F what is linear logic?

Handbook of Constraint Programming

Abstract: Constraint programming is a powerful paradigm for solving combinatorial search problems that draws on a wide range of techniques from artificial intelligence, computer science, databases, programming languages, and operations research. Constraint programming is currently applied with success to many domains, such as scheduling, planning, vehicle routing, configuration, networks, and bioinformatics. The aim of this handbook is to capture the full breadth and depth of the constraint programming field and to be encyclopedic in its scope and coverage. While there are several excellent books on constraint programming, such books necessarily focus on the main notions and techniques and cannot cover also extensions, applications, and languages. The handbook gives a reasonably complete coverage of all these lines of work, based on constraint programming, so that a reader can have a rather precise idea of the whole field and its potential. Of course each line of work is dealt with in a survey-like style, where some details may be neglected in favor of coverage. However, the extensive bibliography of each chapter will help the interested readers to find suitable sources for the missing details. Each chapter of the handbook is intended to be a self-contained survey of a topic, and is written by one or more authors who are leading researchers in the area. The intended audience of the handbook is researchers, graduate students, higher-year undergraduates and practitioners who wish to learn about the state-of-the-art in constraint programming. No prior knowledge about the field is necessary to be able to read the chapters and gather useful knowledge. Researchers from other fields should find in this handbook an effective way to learn about constraint programming and to possibly use some of the constraint programming concepts and techniques in their work, thus providing a means for a fruitful cross-fertilization among different research areas. The handbook is organized in two parts. The first part covers the basic foundations of constraint programming, including the history, the notion of constraint propagation, basic search methods, global constraints, tractability and computational complexity, and important issues in modeling a problem as a constraint problem. The second part covers constraint languages and solver, several useful extensions to the basic framework (such as interval constraints, structured domains, and distributed CSPs), and successful application areas for constraint programming. - Covers the whole field of constraint programming - Survey-style chapters - Five chapters on applications Table of Contents Foreword (Ugo Montanari) Part I : Foundations Chapter 1. Introduction (Francesca Rossi, Peter van Beek, Toby Walsh) Chapter 2. Constraint Satisfaction: An Emerging Paradigm (Eugene C. Freuder, Alan K. Mackworth) Chapter 3. Constraint Propagation (Christian Bessiere) Chapter 4. Backtracking Search Algorithms (Peter van Beek) Chapter 5. Local Search Methods (Holger H. Hoos, Edward Tsang) Chapter 6. Global Constraints (Willem-Jan van Hoeve, Irit Katriel) Chapter 7. Tractable Structures for CSPs (Rina Dechter) Chapter 8. The Complexity of Constraint Languages (David Cohen, Peter Jeavons) Chapter 9. Soft Constraints (Pedro Meseguer, Francesca Rossi, Thomas Schiex) Chapter 10. Symmetry in Constraint Programming (Ian P. Gent, Karen E. Petrie, Jean-Francois Puget) Chapter 11. Modelling (Barbara M. Smith) Part II : Extensions, Languages, and Applications Chapter 12. Constraint Logic Programming (Kim Marriott, Peter J. Stuckey, Mark Wallace) Chapter 13. Constraints in Procedural and Concurrent Languages (Thom Fruehwirth, Laurent Michel, Christian Schulte) Chapter 14. Finite Domain Constraint Programming Systems (Christian Schulte, Mats Carlsson) Chapter 15. Operations Research Methods in Constraint Programming (John Hooker) Chapter 16. Continuous and Interval Constraints(Frederic Benhamou, Laurent Granvilliers) Chapter 17. Constraints over Structured Domains (Carmen Gervet) Chapter 18. Randomness and Structure (Carla Gomes, Toby Walsh) Chapter 19. Temporal CSPs (Manolis Koubarakis) Chapter 20. Distributed Constraint Programming (Boi Faltings) Chapter 21. Uncertainty and Change (Kenneth N. Brown, Ian Miguel) Chapter 22. Constraint-Based Scheduling and Planning (Philippe Baptiste, Philippe Laborie, Claude Le Pape, Wim Nuijten) Chapter 23. Vehicle Routing (Philip Kilby, Paul Shaw) Chapter 24. Configuration (Ulrich Junker) Chapter 25. Constraint Applications in Networks (Helmut Simonis) Chapter 26. Bioinformatics and Constraints (Rolf Backofen, David Gilbert)